Post-hoc Correction Techniques for Constrained Parameter Estimation in Computer Vision

We consider the task of estimating constrained parameters of geometric models which underpin an important class of computer vision problems. A typical model can often be described by two systems of equations, of which one relates image features to parameters, and the other captures internal relationships between the parameters. One way to produce constrained parameters is to first compute an unconstrained estimate by means of the image data and then correct this estimate so that the intra-parameter dependencies are satisfied. This paper focuses on the second stage of estimation and proposes two correction methods applicable to the result of unconstrained minimisation. The performance of the post-hoc correction techniques is evaluated through experiments on estimating the trifocal tensor relating three views of a scene. Results demonstrate that the devised constrained estimators achieve similar accuracy to the maximum likelihood estimator with the advantage of being faster.